If i'm in the resigning FA period and I am trying to trade an arb eligible player, but the other team wants me to sign him long term deal before hand, can I do that after the offer is made or do I have to extend him first them make the offer?

I've done that before. But usually I ask the team to accept the trade first, and then I extend. In case the other team gets cold feet. But yes, you can extend after trade is offered, or while trade is pending.